With the continuous development of GNSS system high-precision positioning, the demand for GNSS positioning grows incessantly in various industries. The conventional real-time kinematic positioning (RTK) technology is widely applied to “static-kinematic” scenarios in engineer application. However, in a “kinematic-kinematic” scenario, the issue of high-precision relative positioning between two moving targets needs to be solved, and the original technology can no longer meet requirements of users. Therefore, a kinematic-to-kinematic differential positioning technology has emerged. In kinematic-to-kinematic differential positioning, the position of a reference station does not need to be known accurately, while a relative position between the reference station and a moving station is the focus of concern. After the ambiguity is fixed correctly, the relative position between the reference station and the moving station can be determined precisely in real time.
Meanwhile, in a highly kinematic situation, for example, during autonomous aerial re-fueling and autonomous landing, high integrity and high accuracy need to be satisfied at the same time. In these application scenarios, it is necessary to use carrier phase measurement to improve precision. Therefore, the issue of position domain integrity of integer ambiguity calculation in a carrier phase measurement quantity in a satellite navigation system is proposed. Generally, it is conservatively assumed that all incorrect fix of ambiguities may lead to high-risk positioning errors. Although such a conservative assumption is simple, it unnecessarily limits the availability of navigation that has strict requirements on integrity and accuracy. Accuracy and integrity risks are basic performance indexes affecting the availability of the navigation system. In the Global Navigation Satellite System (GNSS), the integrity risk refers to a capability of sending an alarm to a user in time when the navigation system cannot be used for a navigation service. In addition, for a new aerospace application, a carrier phase observation quantity needs to be used to ensure that high integrity and high accuracy are satisfied at the same time.
In these application scenarios, to use a kinematic-to-kinematic differential carrier phase measurement quantity, the following problems need to be solved: First of all, in order to implement centimeter-level positioning precision by using carrier phase measurement, the issue of integer ambiguity needs to be solved. In the existing integer ambiguity calculation algorithm, an LAMBDA algorithm, a TCRA algorithm, and a WL-NL algorithm are mainly used. The core idea is to calculate the integer ambiguity by using different combined observation values. However, in some application scenarios with a long baseline distance, a positioning error convergence speed declines, and calculation of the integer ambiguity becomes difficult. The second problem is how to rationally quantify the integrity risk in a kinematic-to-kinematic positioning scenario through carrier phase measurement in satellite navigation. The existing theories are based on the conservative assumption. It is assumed that all incorrectly fixed integer ambiguities lead to a relatively large positioning error, and an integrity risk is calculated based on this condition. Such an assumption greatly limits the availability of the positioning system, and cannot be applied to practical scenarios desirably.
For the first problem, the concept of On The Fly (OTF) was initially proposed by Seeber et al. in 1989. Positioning is implemented by a combined observation quantity of a pseudorange and a carrier phase. Besides, in 1990, Hatch proposed the concept of calculating an integer ambiguity with the least square method, in which an ambiguity space is searched and screened by selecting an optimal combination and a suboptimal combination, to finally calculate the ambiguity. This method is also further developed. In 1992, Abidin et al. optimized the least square search algorithm and proposed an on-the-fly ambiguity calculation method in combination with an ambiguity function method. In 2002, based on the foregoing method, Yang Yunchun et al. developed a single-epoch ambiguity calculation technology. In another type of ambiguity calculation methods, an ambiguity covariance approach is used. Integer ambiguities are searched by using a state vector and a variance-covariance matrix. The least-squares ambiguity decorrelation adjustment method, i.e., the LAMBDA algorithm, is the most commonly used method currently. The LAMBDA algorithm was initially proposed by Teunissen in 1993, and is one of the leading ambiguity calculation methods in use at present. It is generally considered at home and abroad that the LAMBDA algorithm achieves the highest search speed, is most reliable, and is also most compact theoretically. However, in a long-baseline case, it is still difficult to calculate an integer ambiguity in a kinematic-to-kinematic relative positioning scenario. Scholars in Beijing University of Aeronautics and Astronautics proposed an improved method based on the LAMBDA integer ambiguity calculation algorithm. In a short-baseline case, an integer ambiguity is directly calculated by using the LAMBDA algorithm. In a long-baseline case, WL-NL is used to fix integer ambiguities by means of direct rounding, and subsequently, L1 ambiguities can be searched for by using the LAMBDA algorithm after wide-line ambiguities are obtained. The two algorithms are combined, and then ambiguity searching and fixing are performed. Wide-line ambiguities are fixed first, and then narrow-lane L1-frequency ambiguities are calculated by using an ionosphere-free composite model and a wide-lane observation value composite equation, so that the complexity of calculation can be effectively reduced, the calculation load is decreased, and geometric integrity can be ensured, thus facilitating rapid calculation of the integer ambiguity and shortening a convergence time of a positioning error.
For the second problem, with the continuous upgrade of satellite navigation application scenarios, the position domain integrity risk is quantified rationally and the centimeter-level positioning precision is implemented by using carrier phase measurement. A prior probability of correct fix of integer ambiguities may be obtained by correctly fixing the integer ambiguities, and such a probability is referred to as Probability of Correct Fix (PCF). Moreover, the PCF needs to meet the integrity risk requirement. In addition, in the process of calculating the integrity risk, a Probability of Incorrect Fix (PIF) is defined. Besides, a PIF threshold is derived, where the PIF threshold should be distributed from the total navigation integrity risk and be less than the total navigation integrity risk. In a typical positioning navigation process, an ambiguity subset may be determined by merely using a probability lower than the PIF threshold in combination with a probability of incorrect fix, while float solutions of the rest of ambiguities are reserved. Then, partially fixed ambiguities are used to calculate a position estimated value and calculate a corresponding position domain protection level. Finally, the influence of incorrectly fixed ambiguities is evaluated in the position domain to calculate the integrity risk.
In view of the research status of the kinematic-to-kinematic relative positioning and the integrity thereof, and in combination with the conception of the existing methods, this patent proposes an improvement in a long-baseline case based on the LAMBDA integer ambiguity calculation algorithm, to correctly fix integer ambiguities, so that the success rate of ambiguity calculation reaches 99% or higher, and a fixing rate of the integer ambiguities is as high as 97%. After that, the influence caused by incorrectly fixed ambiguities in the position domain is evaluated to define an upper limit of an integrity risk in a navigation process. An integrity threshold calculated based on a partial ambiguity resolution algorithm is proposed. Finally, the integrity calculation in kinematic-to-kinematic relative positioning is implemented.